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Anthony Roberts

Overseas Guest Professors:Anthony Roberts

Name：Anthony Roberts
Title：Professor
Gender：male
Tel：
Email：anthony.roberts@adelaide.edu.au
HomePage：
http://www.maths.adelaide.edu.au/anthony.roberts/index.php
Basic：
Professor
School of Mathematical Sciences
The University of Adelaide, Australia
Educational background：
Work experience：
The University of Adelaide, School of Mathematical Sciences
North Terrace, South Australia
Research fields：
Selected Publications

Large deviation principle for singularly perturbed stochastic damped wave equations. Yan Lv and A.~J. Roberts. Stochastic Analysis and Applications, 32(1):50--60, 2014. doi:10.1080/07362994.2013.838681.
Approximation of the random inertial manifold of singularly perturbed stochastic wave equations. Yan Lv, Wei Wang, and A.~J. Roberts. Stochastics and Dynamics, accepted Aug 08, 2013, to appear Download (draft) article.
Model emergent dynamics in complex systems. A.~J. Roberts. Technical report, [http://www.maths.adelaide.edu.au/anthony.roberts/modelling.php], 2009--2014 Download (draft) article.
Better buffers for patches in macroscale simulation of systems with microscale randomness. J.~E. Bunder, A.~J. Roberts, and I.G. Kevrekidis. Technical report, [http://arxiv.org/abs/1312.1415], Dec 2013.
Macroscale, slowly varying, models emerge from the microscale dynamics in long thin domains. A.~J. Roberts. Technical report, [http://arxiv.org/abs/1310.1541], Dec 2013.
Multiscale modelling couples patches of wave-like simulations. Meng Cao and A.~J. Roberts. In Scott McCue, Tim Moroney, Dann Mallet, and Judith Bunder, editors, Proceedings of the 16th Biennial Computational Techniques and Applications Conference, CTAC-2012, volume 54 of ANZIAM J., pages C153--C170, May 2013. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/6137 [May 14, 2013] Download (draft) article.
Numerical integration of ordinary differential equations with rapidly oscillatory factors. J.~E. Bunder and A.~J. Roberts. Technical report, [http://arxiv.org/abs/1305.5022], May 2013.
Self similarity and attraction in stochastic nonlinear reaction-diffusion systems. Wei Wang and A.~J. Roberts. SIAM J.~Applied Dynamical Systems, 12(1):450--486, 2013 Download (draft) article.
Accurate macroscale modelling of spatial dynamics in multiple dimensions. A.~J. Roberts, Tony MacKenzie, and Judith Bunder. J.~Engineering Mathematics, Online 01-Oct, 2013 Download (draft) article.
Simulating stochastic inertial manifolds by a backward-forward approach. Xingye Kan, Jinqiao Duan, Ioannis~G. Kevrekidis, and A.~J. Roberts. SIAM J.~Appl. Dyn. Systems, 12(1):487--514, 2013. http://arxiv.org/abs/1206.4954 Download (draft) article.
Center manifolds for stochastic evolution equations. Xiaopeng Chen, A.~J. Roberts, and Jinqiao Duan. Technical report, [http://arxiv.org/abs/1210.5924], October 2012 Download (draft) article.
Modify the improved euler scheme to integrate stochastic differential equations. A.~J. Roberts. Technical report, [http://arxiv.org/abs/1210.0933], Oct 2012.
Find centre manifolds of general ordinary differential equations (autonomous). A.~J. Roberts. Technical report, http://www.maths.adelaide.edu.au/anthony.roberts/gencm.php, July 2012 Download (draft) article.
Patch dynamics for macroscale modelling in one dimension. J.~E. Bunder and A.~J. Roberts. In Mark Nelson, Mary Coupland, Harvinder Sidhu, Tara Hamilton, and A.~J. Roberts, editors, Proceedings of the 10th Biennial Engineering Mathematics and Applications Conference, EMAC-2011, volume 53 of ANZIAM J., pages C280--C295, June 2012. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/5074 [June 21, 2012] Download (draft) article.
Averaging approximation to singularly perturbed nonlinear stochastic wave equations. {Yan Lv} and A.~J. Roberts. J.~Math. Phys., 53(6):062702, 2012 Download (draft) article.
Large deviations for slow-fast stochastic partial differential equations. Wei Wang, A.~J. Roberts, and Jinqiao Duan. J.~Differential Equations, 253(12):3501--3522, 2012.
Averaging and deviation for slow-fast stochastic partial differential equations. Wei Wang and A.~J. Roberts. J. Differential Equations, 253:1265--1286, 2012.
Slow manifold and averaging for slow-fast stochastic differential system. Wei Wang and A.~J. Roberts. Journal of Mathematical Analysis and Applications, 398:822--839, 2012. doi:10.1016/j.jmaa.2012.09.029 Download (draft) article.
Macroscopic reduction for stochastic reaction-diffusion equations. Wei Wang and A.~J. Roberts. IMA Journal of Applied Mathematics, published online 16 August, 2012.
Mark Nelson, Anthony~J. Roberts, Mary Coupland, Tara Hamilton, and Harvinder Sidhu, editors. Proceedings of the Engineering Mathematics and Applications Conference, volume 53 of ANZIAM Journal, 2012. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/5172 Download (draft) article.
Diffusion approximation for self-similarity of stochastic advection in {B}urgers' equation. Wei Wang and A.~J. Roberts. Technical report, [http://arxiv.org/abs/1203.0463v1], 2012.
Projective integration of expensive multiscale stochastic simulation. Xiaopeng Chen, A.~J. Roberts, and Ioannis~G. Kevrekidis. In W. McLean and A.~J. Roberts, editors, Proceedings of the 15th Biennial Computational Techniques and Applications Conference, CTAC-2010, volume 52 of ANZIAM J., pages C661--C677, August 2011. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/3764 [August 10, 2011].
Macroscopic discrete modelling of stochastic reaction-diffusion equations on a periodic domain. Wei Wang and A.~J. Roberts. Discrete and Continuous Dynamical System~A, 31(1):253--273, 2011.
Averaging, homogenization and slow manifolds for stochastic partial differential equations. Jinqiao~Q. Duan, A.~J. Roberts, and Wei Wang. In Huaizhong Zhao and Aubrey Truman, editors, New Trends in Stochastic Analysis and Related Topics, volume 12 of Interdisciplinary Mathematical Sciences, chapter 3, pages 95--131. World Scientific, 2011.
On the approximation for singularly perturbed stochastic wave equations. Wei Wang, Yan Lv, and A.~J. Roberts. Technical report, http://arxiv.org/abs/1109.3000, 2011 Download (draft) article.
Computer algebra derives the slow manifold of patch or element dynamics on lattices in two dimensions. Tony MacKenzie and A.~J. Roberts. Technical report, The University of Adelaide, 2011. http://arxiv.org/abs/1102.2037 Download (draft) article.
Scientific achievements：
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